of the Figure of the Earth. 34 1 



equator, the first fraction being f of the other. But, in the case 

 of the earth, the centrifugal force is ff |^ of the gravity at the 

 equator ; and hence, by applying what has just been proved, 

 the equatorial protuberance will be 4 x ^, or ^ of the semi- 

 axis of revolution. It follows therefore that "the polar axis 

 of the earth is to the equatorial diameter, nearly as 229 to 230. 



Newton's determination of the figure of the earth is justly 

 liable to objection in assuming, without proof, that the fluid 

 sphere changes into an oblate elliptical spheroid by the action 

 of the centrifugal force. It is also defective in considering 

 only the extreme case of a fluid mass perfectly homogeneous. 

 It even appears that the illustrious author had not reflected 

 with his usual accuracy on the consequence of an increase of 

 density towards the centre ; for he supposes that it would be 

 attended with a greater oblateness of the spheroid ; which is 

 contrary to what actually happens, as was first proved by 

 Clairaut. 



2 - Huyghens considered the figure of the earth in a diffe- 

 rent point of view, which deserves to be mentioned on account 

 of its connection with the true theory. His attention was 

 first drawn to this subject by the variation in the length of the 

 seconds' pendulum in different latitudes, which was discovered 

 by Richer in 1672. Huyghens immediately perceived that 

 this phenomenon was caused by the centrifugal force at the 

 earth's surface ; which increases in approaching the equator, 

 lessens the power of gravity, and retards the time of the pen- 

 dulum's vibrations. It also occurred to him that if the earth 

 was a perfect sphere, a plumb-line would not be at right an- 

 gles to the sea, or to the surface of standing water, but would 

 be drawn a little aside from the perpendicular by the centri- 

 fugal force. Hence a light body in still water would not 

 press perpendicularly upon the surface, and consequently 

 could not be at rest ; which is contrary to experience. Huy- 

 ghens therefore argued that the earth was not spherical, but 

 protuberant at the equator, in order that the terrestrial meri- 

 dians might be every where perpendicular to the plumb-line. 

 He seems not to have carried his speculations on this subject 

 further, till after the publication of the Principici; when, by 

 adopting Newton's method of equalizing the weights of all 

 the columns reaching from the centre to the surface, he was 

 enabled to determine the figure of the terrestrial meridians. 

 His solution of the problem was first published in an Ap- 

 pendix to a posthumous tract on the cause of gravity. Re- 

 jecting the Newtonian principle of an attraction between the 

 particles, he places, in the centre of the mass, it force attract- 

 ing the particles with the same intensity at all distances: and 



he 



